I think it can have a positive effect on confidence and belief. There can be the added knowledge within a club to help as well.
You also see in individual match-ups ridiculous runs that betray form of the time - such as Spurs record at Stamford Bridge until this season. History arguably put doubt in Spurs players minds and confidence into the Chelsea players for that fixture. Now they have broken that you may see a change in results there.

I think it plays a small factor but people play way too much into this ‘winning mentality’ chat.

Arsenal apparently didn’t have winning mentality before the 1st of 3 Recent FA Cups.
Leicester certainly didn’t before they won the PL.

well even if its not the same players on the pitch chances are theres staff and people around who gained valuable experience n knowledge, surely can't do any harm and could help. The belief breeds around etc too. Don't look that much into it personally but can see how it can have an effect.

It defintely plays a part.

Positive history gives players an extra lift because it gives fans an extra lift.

At the same time, negative history can have the opposite effect.

I think it can have an inspirational effect on a team. But couldn’t you say on the other hand it could add pressure, because there could be more expectation?

High level sports, especially football is decided by the smallest of factors. This psychological factor does play a part. Many times it's repeated over and over again that Team A haven't beat Team B in such a long time etc, and low and behold 9/10 that result repeats itself.

Great contributions guys.

How my first time winners of the CL/European Cup have there been in the last 20 years? Just Chelsea?

Certainly looks like history plays a role.